Error Ellipse Research Articles

Study on the rigorous accuracy of any point on a linear element

In order to obtain the rigorous accuracy of any point on the straight line element, based on existing research, this article considers the error of the straight line element and the error of any point to its end point of the straight line element, attempts to discuss the accuracy calculation of any point on the straight line element in three different situations, and through case analysis, compares the position covariance matrix of any point on the straight line element in three situations and draws its error ellipse using MATLAB programming. Finally, different accuracy sizes and different error ellipses are obtained. This research has certain guiding significance and role for error calculation in precision engineering measurement, such as large bridges or large through projects.

TDOA-based localization of cracking sound events with minimal-error microphone subsets

We present a method based on the time difference of arrival (TDOA) and index minimal-error subsets of microphones to localize sudden cracking sound events, which appear somewhere in flax-fiber reinforced concrete specimens. Validation tests with small-scale pendulum impacts and known impact locations were carried out. Error estimation was performed and error ellipses were calculated. Microphone subsets leading to the smallest localization error were indexed. We validated the localization accuracy against localization results calculated using the delay-and-sum beamforming technique. Further, tension tests on concrete specimens were performed until failure; crack patterns were recorded by photogrammetry. The cracking sound events were localized. With the good match between TDOA-based localization results and crack patterns, we demonstrate that the proposed localization procedure is reliably applicable for real-time localization of concrete cracking.

Autonomous wireless positioning system using crowdsourced Wi-Fi fingerprinting and self-detected FTM stations

Wi-Fi positioning system (WPS) has been proven as an effective way to realize universal indoor navigation for smart city-related applications. The localization ability of the existing WPS is affected by the low precision of the crowdsourced database and the unknown location of local wireless stations. This paper develops an integrated indoor localization framework using crowdsourced Wi-Fi fingerprinting and self-detected Wi-Fi Fine Time Measurement (FTM) stations (IL-CFSW). A novel crowdsourced mobile sensors data modeling algorithm with self-calibrated parameters is proposed, and modeled trajectories are further segmented and matched with the existing pedestrian indoor network to enhance the performance of the final database generation. Furthermore, the iteration unscented Kalman filter (iUKF) is adopted to recognize the position and calibrate the bias of existing Wi-Fi FTM anchors combined with the hybrid distance measurement model. Finally, an enhanced particle filter with error ellipse constraint is developed to fuse different location sources and indoor network information. Comprehensive experimental results present that the developed IL-CFSW can achieve autonomous 3D indoor localization performance in multi-floor contained scenes and meter-level positioning accuracy is achieved with the consideration of pedestrian indoor network information.

Идентификация эллипса ошибок и подеры эллипса ошибок по элементам ковариационной матрицы

The authors present a study of the point position mistake relationship with the elements of the error ellipse. The comparison of the mentioned error, determined by the F. R. Helmert’s and P. Werkmeister’s formulas, is given. It is shown that they both are related to the elements of the error ellipse and the covariance matrix of the coordinate vector. For the conditions of the polar serif, the dependence of the correlation coefficient of the determined point coordinates on the directional angle of the line to this point, as well as that of the angular and linear measurements mutual accuracy, is established. The relationships between the elements of the covariance matrix and those of the ellipse of point position errors are investigated for various special cases. Namely, when the correlation coefficient is zero, it is ± 1, in the case of equality of the determined point’s inverse weight matrix diagonal elements and when the determination of the point’s position was performed by a polar serif. The error ellipse dimension is considered as a function of linear COEX systems in all directions. Its graphs and subtypes are presented depending on the determined point’s inverse weight matrix elements values

Reactivation of Ramadi-Musaiyib Fault-Najd Faults System, Iraq

Nine earthquakes inside Mesopotamia Plain from 2016 to 2018 were analyzed. Three seismic networks have been relied on to relocate these events and know their responsible fault. These networks are; Mesopotamian Seismological Center, Al-Refaei Seismic Array and Iranian Seismological Center. The results showed that the root mean square (RMS) values for all relocated events ranged between 0.002-0.997. The results of the error ellipse ranged from 0.24 - 4.17 km with longitude and 0.76 - 8.24 km with latitude. The new locations of these events are on or near the Ramadi-Musaiyib Fault. This means that the Ramadi-Musaiyib Fault, which belongs to the Najd fault system, is currently in reactivation.

Estimation of pop-up satellite archival tag initial surface position: applications for eastern Bering Sea crab research

BackgroundClimate change is reshaping Bering Sea crab distributions and recent population declines have elevated the urgency in understanding spatial dynamics in relation to management boundaries. While pop-up satellite archival tags (PSATs) can provide fishery-independent movement information, a high level of spatial resolution is needed to evaluate small-scale (i.e., 10 s of km) movements of crabs. Because PSATs drift at the surface prior to acquisition of a satellite-estimated location (via Argos), the accuracy of pop-up location (i.e., animal terminal position) estimates depends on the ability to accurately estimate drift error. We deployed PSATs (n = 36) on fixed-position moorings in Bristol Bay and Marmot Bay, Alaska to validate a new method to estimate tag pop-up location and an associated error ellipse that uses in situ drift data from surfaced tags to estimate drift error. Estimated pop-up location was compared to the location of tag surfacing (i.e., the tag’s fixed position) and to an alternative estimate (i.e., an early satellite-estimated location). Additional tags were deployed on mature male red king crab (Paralithodes camtschaticus) in Bristol Bay during 2020 (n = 84) and 2021 (n = 90) to compare estimates of tag drift error and crab displacement derived using the method.ResultsFor red king crab tags with pop-up location estimates in 2020 (n = 79) and 2021 (n = 46), mean drift error was 9% and 44% of mean crab displacement, respectively. For fixed-position PSATs with pop-up location estimates (n = 27), mean distance between the estimated pop-up location and the tag’s fixed position was 2.0 km, representing a mean improvement in accuracy of 51% over alternative estimates. Corresponding error ellipse estimates either encompassed the tag’s fixed position (n = 11) or their boundaries were a mean distance of 1.3 km (n = 16) from the fixed position.ConclusionsOur method improves pop-up location estimates for PSAT-tagged animals and is particularly well suited for crabs and other slow-moving benthic marine species. The improved estimates enhance PSAT utility for addressing management and ecological questions that require a fine spatial resolution, such as movement near management boundaries or defining essential habitat for important life history events.

Searching for X-ray counterparts of unassociated Fermi-LAT sources and rotation-powered pulsars with SRG/eROSITA

Context. The latest source catalog of the Fermi-LAT telescope contains more than 7000 γ-ray sources at giga-electronvolt energies, with the two dominant source classes thought to be blazars and rotation-powered pulsars. Despite continuous follow-up efforts, around 2600 sources have no known multiwavelength association. Aims. Our target is the identification of possible (young and recycled) pulsar candidates in the sample of unassociated γ-ray sources via their characteristic X-ray and γ-ray emission. To achieve this, we cross-matched the Fermi-LAT catalog with the catalog of X-ray sources in the western Galactic hemisphere from the first four all-sky surveys of eROSITA on the Spektrum-Roentgen-Gamma (SRG) mission. We complement this by identifying X-ray counterparts of known pulsars detected at γ-ray and radio energies in the eROSITA data. Methods. We used a Bayesian cross-matching scheme to construct a probabilistic catalog of possible pulsar-type X-ray counterparts to Fermi-LAT sources. Our method combines the overlap of X-ray and γ-ray source positions with a probabilistic classification (into pulsar and blazar candidates) of each source based on its γ-ray properties and a prediction on the X-ray flux of pulsar- or blazar-type counterparts. Finally, an optical and infrared counterpart search was performed to exclude coronally emitting stars and active galactic nuclei from our catalog. Results. We provide a catalog of our prior γ-ray-based classifications of all 2600 unassociated sources in the Fermi-LAT catalog, with around equal numbers of pulsar and blazar candidates. Our final list of candidate X-ray counterparts to suspected new high-energy pulsars, cleaned for spurious detections and sources with obvious non-pulsar counterparts, contains around 900 X-ray sources, the vast majority of which lie in the 95% γ-ray error ellipse. We predict between 30 and 40 new pulsars among our top 200 candidates, with around equal numbers of young and recycled pulsars. This candidate list may serve as input to future follow-up campaigns, looking directly for pulsations or for the orbital modulation of possible binary companions, where it may allow for a drastic reduction in the number of candidate locations to search. We furthermore detect the X-ray counterparts of 15 known rotation-powered pulsars, which were not seen in X-rays before.

Uncertainty assessment of machine tool squareness error identification using on-machine measurement

Identification and compensation of geometric errors in the machine tool are widely performed to increase machining accuracy. Periodic verification of the geometric errors, as introduced in ISO 230-2, helps monitor the machine tool accuracy during continued manufacturing operation and detect accuracy degradation early on. While interferometry-based error identification techniques are commonly applied, on-machine measurement (OMM), with its increasing availability to machine tools, can be used to identify geometric errors as an alternative to traditional interferometry-based techniques. As geometric errors also contribute to OMM error, assessment of the uncertainty of error identification is essential to ensure the reliability of the identification. This work presents a method to evaluate the uncertainty in the OMM-based geometric error identification process by Monte Carlo simulation. The error ellipse model, which represents OMM errors with better accuracy, is utilized to improve the identification uncertainty. The squareness errors, as position-independent geometric errors that contribute to machining inaccuracy, are taken as an example to demonstrate the presented method. The influence of the artifact setup errors on the error identification is also investigated. A series of experiments are conducted to evaluate the uncertainty of the OMM-based identification method. The geometric error obtained with the presented method is found to deviate by less than 10% from that obtained with an interferometry-based commercial instrument. The uncertainty obtained from the proposed Monte Carlo simulation method matches well with the uncertainty results obtained by the Guide to the Expression of Uncertainty in Measurement method and repeated measurements.

Increasing of the accuracy of determining the coordinates of an aerial object in the two-position network of small-sized radars

The object of research is the process of determining the coordinates of aerial objects by a small-sized radars. The main hypothesis of the study assumes that combining two small-sized radars into a network could improve the accuracy of determining the coordinates of aerial objects. It was established that when determining the coordinates of an aerial object by a small-sized radars, the accuracy of determining the range is much better than the accuracy of determining the angular coordinate. To eliminate this shortcoming, a two-position network of small-sized radars and their error ellipses was considered. It is proposed to use the range-finding method in each small-sized radar station of the two-position network. A method for determining the coordinates of aerial objects in a two-position network of small-sized radars has been improved, which, unlike known ones: – enables a synchronous survey of the airspace by small-sized radars; – measures the range to the aerial object by two small-sized radars; – determines the coordinates of the aerial object by the joint processing of radar information from two small-sized radars. The accuracy of determining the coordinates of aerial objects in a two-position network of small-sized radars was evaluated. The experimental evaluation was carried out by means of simulation using the method of Monte Carlo statistical tests. Working areas of the two-position network of small-sized radars were calculated. It was established that the two-position network of small-radars works only in the area formed by the intersections of the viewing areas of small-sized radars during their autonomous operation.

Cosmological constraints from low redshift 21 cm intensity mapping with machine learning

ABSTRACT The future 21 cm intensity mapping observations constitute a promising way to trace the matter distribution of the Universe and probe cosmology. Here, we assess its capability for cosmological constraints using as a case study the BINGO radio telescope, that will survey the Universe at low redshifts (0.13 < z < 0.45). We use neural networks (NNs) to map summary statistics, namely, the angular power spectrum (APS) and the Minkowski functionals (MFs), calculated from simulations into cosmological parameters. Our simulations span a wide grid of cosmologies, sampled under the ΛCDM scenario, {Ωc, h}, and under an extension assuming the Chevallier–Polarski–Linder (CPL) parametrization, {Ωc, h, w0, wa}. In general, NNs trained over APS outperform those using MFs, while their combination provides 27 per cent (5 per cent) tighter error ellipse in the Ωc–h plane under the ΛCDM scenario (CPL parametrization) compared to the individual use of the APS. Their combination allows predicting Ωc and h with 4.9 and 1.6 per cent fractional errors, respectively, which increases to 6.4 and 3.7 per cent under CPL parametrization. Although we find large bias on wa estimates, we still predict w0 with 24.3 per cent error. We also confirm our results to be robust to foreground contamination, besides finding the instrumental noise to cause the greater impact on the predictions. Still, our results illustrate the capability of future low-redshift 21 cm observations in providing competitive cosmological constraints using NNs, showing the ease of combining different summary statistics.

Swift Follow-up of Reported Radio Pulsars at Fermi 4FGL Unassociated Sources

Following the discovery of radio pulsars at the position of Fermi-LAT unassociated sources by the TRAPUM group, we conduct Swift-XRT observations of six of those 4FGL sources to determine if any pulsar-like X-ray sources are present and to confirm the reported detection of an X-ray counterpart via eROSITA at 4FGL J1803.1−6708. At two of the six targets, we detect no X-ray sources at the TRAPUM radio position, placing an upper limit on the 0.3–10.0 keV flux. At 4FGL J1803.1−6708 we find an X-ray source at the TRAPUM and eROSITA position. At 4FGL J1858.3−5424 we find a new X-ray counterpart at the TRAPUM position with signal-to-noise ratio S/N = 4.17, but also detect a distinct and separate X-ray source. At 4FGL J1823.8−3544 and 4FGL J1906.4−1757 we detect no X-ray flux at the TRAPUM positions, but we do detect separate X-ray sources elsewhere in the Fermi error ellipse. At these last two targets, our newly detected Swift sources are possible alternatives to the radio pulsar associations proposed by TRAPUM. Our findings confirm several of the discoveries reported by the TRAPUM group but suggest that further observations and investigations are necessary to confirm the low-energy counterpart of several unassociated sources.

Unraveling the formation histories of the first supermassive black holes with the Square Kilometre Array’s pulsar timing array

Galaxy mergers at high redshifts trigger activity of their central supermassive black holes, eventually also leading to their coalescence as well as a potential source of low-frequency gravitational waves detectable by the Square Kilometre Array’s pulsar timing array (SKA PTA). Two key parameters related to the fueling of black holes are the Eddington ratio of quasar accretion,ηEdd, and the radiative efficiency of the accretion process,ϵ(which affects the so-called active lifetime of the quasar,tQSO). Here, we forecast the regime of detectability of gravitational wave events with SKA PTA. We find the associated binaries to have orbital periods of the order of weeks to years, observable via relativistic Doppler velocity boosting and/or optical variability of their light curves. Combining the SKA regime of detectability with the latest observational constraints on high-redshift black hole mass and luminosity functions, as well as theoretically motivated prescriptions for the merger rates of dark matter halos, we forecast the number of active counterparts of SKA PTA events expected as a function of primary black hole mass atz ≳ 6. We find that the quasar counterpart of the most massive black holes will be uniquely localizable within the SKA PTA error ellipse atz ≳ 6. We also forecast the number of expected counterparts as a function of the quasars’ Eddington ratios and active lifetimes. Our results show that SKA PTA detections can place robust constraints on the seeding and growth mechanisms of the first supermassive black holes.

The Scaling Ellipsoid Method to Calculate Wellbore Separation Factors

The wellbore separation factor is the most common index to evaluate wellbore collision risk. However, all existing calculation methods of separation factor can only evaluate the separation degree of two error ellipses on some plane, and cannot directly evaluate the separation degree of two error ellipsoids in 3D space. These methods will lead to over-optimistic or over-conservative assessments inevitably, and cannot satisfy the wellbore collision avoidance requirements. Therefore, a new calculation method for the wellbore separation factor is presented, which is named as Scaling Ellipsoid Method (SEM). The new method references the Expansion Ellipse Method (EEM) and expands or contracts two error ellipsoids by the same scaling factor up to the exterior contact condition. Then the scaling factor is selected as the wellbore separation factor. SEM can directly and accurately evaluate the separation degree of two error ellipsoids in 3D space. A mathematical model to calculate the SEM separation factor (SESF) characterized by a quadratic equation set with four unknowns is established, and its numerical solution method and optimization tactics are presented to enhance its solution efficiency. Instance analyses have shown that SEM can preferably evaluate wellbore collision risk, contribute to pinpointing dangerous intervals, and decrease the anti-collision workloads.

Deep Synoptic Array Science: Discovery of the Host Galaxy of FRB 20220912A

We report the detection and interferometric localization of the repeating fast radio burst (FRB) source FRB 20220912A during commissioning observations with the Deep Synoptic Array (DSA-110). Two bursts were detected from FRB 20220912A, one each on 2022 October 18 and 2022 October 25. The best-fit position is (R.A. J2000, decl. J2000) = (23:09:04.9, +48:42:25.4), with a 90% confidence error ellipse with radii ±2″ and ±1″ in R.A. and decl., respectively. The two bursts are polarized, and we find a Faraday rotation measure that is consistent with the low value of +0.6 rad m−2 reported by CHIME/FRB. The DSA-110 localization overlaps with the galaxy PSO J347.2702+48.7066 at a redshift z = 0.0771, which we identify as the likely host. PSO J347.2702+48.7066 has a stellar mass of approximately 1010 M ⊙, modest internal dust extinction, and a star formation rate likely in excess of 0.1 M ⊙ yr−1. The host-galaxy contribution to the dispersion measure is likely ≲50 pc cm−3. The FRB 20220912A source is therefore likely viewed along a tenuous plasma column through the host galaxy.

Mission Analysis for Landing on Pluto from a Fast, Hyperbolic Trajectory

The results of a Pluto landing analysis study for a fast, hyperbolic approach trajectory are presented by assuming the use of a novel entry, descent, and landing system called an enveloping aerodynamic decelerator. A landing site uncertainty analysis is performed for an 11 September 2040 arrival by means of a Monte Carlo simulation to map key trajectory, aerodynamic, system, and atmosphere uncertainties to landing zone errors. The estimated 3 landing error ellipse is about 430 by 190 km. The band of feasible landing sites is between 35°N and 10°S latitude on the surface of Pluto.

Response nonuniformity modelling for colour imaging systems

In this paper, a theoretical analysis reveals that system radiation transmission nonuniformity and system radiation conversion nonuniformity have different forms. A colour imaging system response nonuniformity model is then proposed according to the two kind of nonuniformity of three channels. The model includes two models, one for brightness and one for chromaticity. The brightness model is built according to the nonuniformity of single channel. The chromaticity model is built as an error ellipse in the chromaticity diagram. The error ellipse can be also used as a representation parameter of the radiation conversion nonuniformity. The proposed models were verified using three commercial digital cameras. The experimental results show that the proposed nonuniformity model is correct. Moreover, the proposed representation parameter is an effective way to evaluate and characterize the nonuniformity of a colour imaging system. This research has value as a reference for the correction and evaluation of response nonuniformity in colour imaging systems.

A Safe Decision Making Framework for Automated Vehicle Navigation among Human Drivers

In the near future, automated vehicles (AVs) will have to interact closely with Human-driven vehicles (HDVs). This work proposes an integrated decision-making framework that considers HDVs motion, a feasibility check, and planning. A learning-based encoder-decoder Long Short-Term Memory is used for HDV motion prediction. An error ellipse is used to capture the uncertainty from the learning-based model. A feasibility check is carried out to confirm the existence of a lane change trajectory from the given target vehicle's future position. The results from the feasibility check decide the action of AV. This work uses a lower-order parametric curve for path planning combined with an efficient trapezoidal acceleration-based velocity planner. Simulation results show that the proposed method guarantees a collision-free path for a lane changing scenario, given the lead vehicle position.

Earthquake on August 6, 2022 in the zone of the West Timan overthrust

On August 6, 2022, an earthquake was registered in Komi Republic, in the Udora district. Data from 17 seismic stations with epicentral distances from 227 to 1142 km were involved in processing the seismic event on August 6. The azimuth environment is uneven, the maximum azimuth gap is GAP=111.8°. As a result of instrumental processing, the following parameters were obtained: coordinates 64.023°N, 50.091°E, time at the source t0 =10:21:32 (UTC), depth h=14 km, energy class according to T.G. Rautian KR=10.2, local magnitude ML=3.6, error ellipse Azmajor=40°, Rminor=6.2 km, Rmajor=10.5 km. According to our calculations, the seismic event occurred in the middle reaches of the river Mezen, on the territory of the state natural reserve of regional significance “Udorsky”. The nearest settlements to the epicenter are located only 50 km away and the residents did not feel the earthquake. This area is not mining, so the seismic event is classified by us as a “tectonic earthquake”. The earthquake is confined to the West Timan thrust zone, which is a collision suture of the Russian and Pechora plates. The source at a depth of 14 km is located in the region of pericratonic subsidence covering the northeastern margin of the Russian Plate and the Kanino-Timan belt; on the boundary of the basement of the Mezen syneclise and the Timanid complex thrust over it. The earthquake may have been caused by tectonic pressure from the Pechora plate. This is the first earthquake in the West Timan thrust zone. Earthquakes occur mainly in the northeast of the Russian Plate, within the Volga-Ural anteclise, Mezen and Moscow syneclise. In addition, although the recorded earthquakes are mostly low-magnitude, they reflect the modern tectonic activation of the earth’s crust.

Optimal Geometries for AOA Localization in the Bayesian Sense

This paper considers the optimal sensor placement problem for angle-of-arrival (AOA) target localization in the 2D plane with a Gaussian prior. Optimal sensor locations are analytically determined for a single AOA sensor using the D- and A-optimality criteria and an approximation of the Bayesian Fisher information matrix (BFIM). Optimal sensor placement is shown to align with the minor axis of the prior covariance error ellipse for both optimality criteria. The approximate BFIM is argued to be valid for a sufficiently small prior covariance compared with the target range. Optimal sensor placement results obtained for Bayesian target localization are extended to manoeuvring target tracking. For sensor trajectory optimization subject to turn-rate constraints, numerical search methods based on the D- and A-optimality criteria as well as a new closed-form projection algorithm that aims to achieve alignment with the minor axis of the prior error ellipse are proposed. It is observed that the two optimality criteria generate significantly different optimal sensor trajectories despite having the same optimal sensor placement for the localization of a stationary target. Analysis results and the performance of the sensor trajectory optimization methods are demonstrated with simulation examples. It is observed that the new closed-form projection algorithm achieves superior tracking performance compared with the two numerical search methods.

A blazar candidate for the Fermi source 4FGL J1848.7–0129

Abstract The Fermi source 4FGL J1848.7–0129 has been historically related to the globular cluster GLIMPSE-C01 since its very first detection. Although this association is widely accepted, as it appears in the most recent Fermi catalogue, it deserves to be revisited given the multiwavelength evidences and the recent discovery of variable X-ray sources in the Fermi source region. In particular, low frequency radio maps from the Giant Metre Radio Telescope in Pune (India) have been carefully inspected which, together with X-ray data re-analysis from Chandra, lead us to get a deep insight into the candidates to be associated to 4FGL J1848.7–0129. This results in the discovery of a new X-ray variable point source coincident with an unreported non-thermal radio emitter, both of them well inside the 4FGL J1848.7–0129 error ellipse. We analyse and discuss all these observational facts, and we propose now a newly discovered blazar candidate as the most promising responsible for the gamma-ray emission in the Fermi source. If confirmed, this result would set constrains on the number of millisecond pulsars in GLIMPSE-C01 or their gamma-ray emission properties.